Friday, June 12, 2009

Fermat's Last Theorem

Pierre de Fermat (1601-1665) was a French mathematician who, together with Isaac Newton and Gottfried Leibnitz, is credited with the invention of calculus (calculations which allow the mathematical description of two factors relative to each other). He also made notable contributions to analytic geometry, probability, and optics. His first love, however, was number theory - the philosophy of mathematics. He was more interested in solving and setting problems, rather than his own fame and fortune.

One of these, "Fermat's Last Theorem" (named as such because it became the last of his theorems requiring proof), states that no three positive integers x, y, and z can satisfy the equation x^n + y^n = z^n for any integer value of n greater than two. Fermat set the challenge for mathematicians to prove the theorem correct. In a scientific sense, it can't be proved, since this would involve testing an infinite series of numbers. However, maths provides the opportunity to prove a theorem without the limitations of perception, and therefore is considered the purest form of truth and knowledge. Despite the simplicity of the equation, for three hundred years, the challenge beat all of the best minds in the world. Tantalisingly, Fermat left some indications when he died that he had come up with the proof himself. In 1995, softly spoken British mathematician Andrew Wiles, a maths professor at Princeton University, gave a talk at a conference at Cambridge in which he claimed to have met Fermat's challenge. It was the culmination of thirty years of work. He'd been fascinated by the probem since he came across it in a library book at the age of ten. The documentary below shows what was involved in him producing his proof, and the nightmare that resulted from it:

No comments: